Kinetic Molecular Theory Flashcards
Assumptions
Gas consists of molecules of mass m.
Gas has random motion.
Straight line movement between collisions.
Size of molecules is negligible
Molecules not interacting which undergo perfectly elastic collisions
Evidence of molecular motion
Flow: Gases flow to fill a volume
Evidence of molecular motion (Thermal Expansion)
When a gas is heated, particles will move faster and push outwards more
Evidence of molecular motion (Brownian Motion)
This is when small particles move randomly due to many collisions
Evidence of molecular motion (Diffusion)
This is the transport of matter through a gas, we see this when gases mix
Origin of pressure
Molecular collisions with wall of container create pressure. The collisions experience a change in momentum, this change in momentum is the pressure.
Momentum = mass*velocity
Kinetic energy of a single molecule (equation)
E(KE) = 1/2 (ms^2)
Mean Kinetic energy per molecule (equation)
Line(E(KE)) = 1/2 (mc^2), this equation is derived from:
pV = 1/3nNa(mc^2)
Combining kinetic theory and ideal gas
pV = 1/3nNa(mc^2) & pV = nRT.
c^2 = 3RT/Mr, where Mr is the molar mass.
c = root(3RT/Mr)
Graham’s law of effusion
At a given temperature and pressure the rate of effusion is inversely proportional to the square root of the molar mass.
Rate of effusion = 1/root(Mr)
Small Mr = More effusion
Mixing of two gases (equation)
Rate of effusion A/Rate of effusion of B which is the same as equation:
Mixing of two gases = (Ma/Mb)^1/2, where Ma, Mb are molar masses wrt. their reactants A and B
Define Effusion
Effusion is when a gas is escaping through a hole
Define Diffusion
This is when different gases are mixing
Collision cross-section (equation)
(pi)diameter^2 = pi(2radius)^2 = sigma
Collision frequency (equation)
z = root(2)Na(c(sigma))(p/RT)
Mean free path (equation) and exception
lambda = RT/ [root(2)NaSigma*p],
Please note that this equation is for systems where molecules are considered as hard spheres. (Ideal Gases)
Phase transition diagram
Phase transition is when the graph(line) is horizontal left to right at a given pressure.
Define a Real Gas
Real gases cannot be an ideal gas, these gases DO have attractions between molecules
Van der Waals equation (Real Gases)
(p+a(n/V)^2)(V-n*b) = nRT
where, a accounts for intermolecular interactions and b accounts for the finite size of molecules
Temperature (a & b)
T(subscript c) = 8a/27Rb
Pressure (a & b)
P(subscript c) = a/27b^2
Volume (a & b)
V(subscript c) = 3b
What is a and b?
a: Attractive interactions
b: Real volume of molecules in a gas
Interactions present in a real gases & sticky collisions
Hydrogen Bonding
London Dispersion
Dipole-Dipole Interactions
Dipole Induced (This causes sticky collisions)
